Depends on your definition of furthest away (points, places, percentage of points). There have been some huge differences, the biggest I know are:
1963 Clark 54, Taylor 1. Teammate 15th, 53 points difference, Clark scored actually 73 points, but only 6 results counted, so you could say difference is 72. I'm not sure if Taylor was really Clarks teammate though.
1981 Piquet 50, Rebaque 11. Teammate 10th place, 39 points difference.
1982 Rosberg 44, Daly 8. Teammate 13th place, 36 points difference. Daly didn't do all the races though. Reutemann scored 6 points in 2 races (16th), Andretti no points in one race (funny one, actually a former WDC that didn't score while his teammate went on to win the WDC. He only drove one race for Williams that year, later he drove two for Ferrari, in one of which he scored 4 points, so I wouldn't take this one too seriously).
1983 Piquet 59, Patrese 13 (including a gifted win, Piquet was leading, but dropped to 3th, because that was enough for the WDC). Teammate 9th place, 46 points difference.
1985 Prost 73, Lauda 14. Teammate 10th place, 59 points difference. A (reigning!) WDC thoroughly beaten by his teammate.
It also depends on your definition of teammate: must he race the whole year for the team, or are a few races (or even one) enough. And what if they have a customer car?
There's probably somewhere a teammate that scored no points while his teamleader got crowned WDC (I already mentioned Andrette above). In 1970 Rindt had several teammates. I'm not sure who they were and if they scored points while racing with Rindt. Fittipaldi scored 13 points, but won after Rindt had died, so during Rindts 'races he only scored 4 points (in his first race, he raced two races while Rindt was living, not counting Italy). Wisell also drove for Lotus that year, but scored 4 points after Rindt died, not sure if he drove for Lotus while Rindt was living. And Miles drove a Lotus and scored 2 points in the first race of that year. I'm too lazy to look up the details.